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The paper introduces Cognitive Loop of Thought (CLoT), a novel Chain-of-Thought framework based on Reversible Hierarchical Markov Chains, to improve the efficiency and robustness of mathematical reasoning in LLMs. CLoT decomposes problems into hierarchical sub-problems with backward verification at each layer, mitigating error propagation and enabling context-aware reasoning. Experiments on mathematical benchmarks show that CLoT outperforms traditional CoT and CoT-SC, achieving 99.0% accuracy on the AddSub dataset using GPT-4o-mini.
LLMs can achieve state-of-the-art mathematical reasoning accuracy while pruning redundant computations by verifying solutions in a hierarchical, reversible manner.
Multi-step Chain-of-Thought (CoT) has significantly advanced the mathematical reasoning capabilities of LLMs by leveraging explicit reasoning steps. However, the widespread adoption of Long CoT often results in sequence lengths that exceed manageable computational limits. While existing approaches attempt to alleviate this by reducing KV Cache redundancy via Markov chain-like structures, they introduce two critical limitations: inherent memorylessness (loss of context) and limited backward reasoning capability. To address these limitations, we propose a novel Chain-of-Thought framework based on Reversible Hierarchical Markov Chain, termed Cognitive Loop of Thought (CLoT), and a backward reasoning dataset CLoT-Instruct. In CLoT, problems are decomposed into sub-problems with hierarchical dependencies. Inspired by human cognitive processes, we introduce a backward verification mechanism at each hierarchical layer. Furthermore, we implement a pruning strategy: once higher-level sub-problems are verified, redundant lower-level sub-problems are pruned to maximize efficiency. This approach effectively mitigates error propagation and enhances reasoning robustness. Experiments on four mathematical benchmarks demonstrate the effectiveness of our method. Notably, on the AddSub dataset using GPT-4o-mini, CLoT achieves 99.0% accuracy, outperforming traditional CoT and CoT-SC by 4.1% and 2.9%, respectively.
